The study of round-trip time (RTT) measurements on the Internet is of particular importance for improving real-time applications, enforcing QoS with traffic engineering, or detecting unexpected network conditions. On large timescales, from 1 hour to several days, RTT measurements exhibit characteristic patterns due to inter and intra-AS routing changes and traffic engineering, in addition to link congestion. We propose the use of a nonparametric Bayesian model, the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM), to characterize RTT timeseries. The parameters of the HMM, including the number of states, as well as the values of hidden states are estimated from delay observations by Gibbs sampling. No assumptions are made on the number of states, and a nonparametric mixture model is used to represent a wide range of delay distribution in each state for more flexibility. We validate the model through three applications: on RIPE Atlas measurements we show that 80% of the states learned on RTTs match only one AS path; on a labelled delay changepoint dataset we show that the model is competitive with state-of-the-art changepoint detection methods in terms of precision and recall; and we show that the predictive ability of the model allows us to reduce the monitoring cost by 90% in routing overlays using Markov decision processes.